# Example of charge distribution that nullifies the electric field in a finite region

Since I'm trying to understand why the electric field is null inside a charged conductor, and the explanation usually given is that "the charges rearrange themeselves in such a way as to nullify the electric field inside the conductor", what I need is an example of continuous charge distribution for which the electric field is null in a finite region.

If I consider the Poisson's equation inside a conductor, what I get by enforcing V = constant is that $$\bigtriangleup V = 0$$ and then $$\rho=0$$. So I'm confused

I would be happy to have an answer just for the case of a spherical region.

Or, you could provide a link to a mathematical proof for the existence of an equilibrium configuration for a set of charged particles constrained in a finite region

• There is no field in the interior of a uniformly charged spherical shell... Feb 15, 2021 at 20:22
• The charge distribution in a perfect conductor is not continuous at the boundaries, so the Laplacian in Poisson's equation is not really meaningful there. Feb 15, 2021 at 20:27